Solve for $x$ and $y$ using elimination. ${-x-3y = -11}$ ${x+5y = 15}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-x-3y = -11}\thinspace$ to find $x$ ${-x - 3}{(2)}{= -11}$ $-x-6 = -11$ $-x-6{+6} = -11{+6}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 2}$ into $\thinspace {x+5y = 15}\thinspace$ and get the same answer for $x$ : ${x + 5}{(2)}{= 15}$ ${x = 5}$